A Structured Neural ODE Approach for Real Time Evaluation of AC Losses in 3D Superconducting Tapes

TL;DR

Problem: real-time evaluation of AC losses in HTS cables with nonlinear IEM models is computationally expensive. Approach: apply POD-DEIM and a Structured Neural ODE that learns nonlinear reduced dynamics in the reduced order space of the $J$-$\varphi_e$ formulation; results show the Structured model achieves large online speedups with comparable or superior accuracy to POD-DEIM across multiple test regimes. Contributions: first application of POD-DEIM to IEM-based HTS models, and a physics-informed latent-dynamics ROM that preserves problem structure while remaining nonintrusive. Impact: enables real-time quench monitoring and paves the way for multiphysics couplings with thermal solvers for integrated design and control.

Abstract

Efficient modeling of High Temperature Superconductors (HTS) is crucial for real-time quench monitoring; however, full-order electromagnetic simulations remain prohibitively costly due to the strong nonlinearities. Conventional reduced-order methods, such as the Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM), alleviate this cost but are limited by intrusive implementation and by the need for many interpolation points. This work investigates reduced-order strategies for Integral Equation Method (IEM) of HTS systems. We present the first application of POD-DEIM to IEM-based HTS models, and introduce a Structured Neural Ordinary Differential Equation (Neural ODE) approach that learns nonlinear dynamics directly in the reduced space. Benchmark results show that the Neural ODE outperforms POD-DEIM in both efficiency and accuracy, highlighting its potential for real-time superconducting simulations.

Figures (7)

• Figure 1: Resulting 2D mesh of the cable under analysis.
• Figure 2: Graphical representation of the training process. Green arrows illustrate the discrepancy between the true state values and the predicted values, which the optimization procedure seeks to minimize.
• Figure 3: Singular value decay of the current, potential, and nonlinear term $\mathbf{R}(\mathbf{i})\mathbf{i}$ snapshot matrices. Retained modes are shown in orange, discarded modes in blue.
• Figure 4: Top: Evolution of selected current states in the within-the-distribution validation transient for the simulations (dashed red) compared to the (solid blue). Bottom: Corresponding mean, 95th-percentile, and maximum errors between the s and the .
• Figure 5: Comparison between the current density map of the simulation and the -based on the within-the-distribution validation transient. The results demonstrate high accuracy.